IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i19p4109-d1250172.html
   My bibliography  Save this article

Vibrations of Nonlocal Polymer-GPL Plates at Nanoscale: Application of a Quasi-3D Plate Model

Author

Listed:
  • Yunhe Zou

    (School of Mechanical Engineering, Inner Mongolia University of Technology, Hohhot 010051, China
    Inner Mongolia Key Laboratory of Special Service Intelligent Robotics, Hohhot 010051, China)

  • Yaser Kiani

    (Faculty of Engineering, Shahrekord Univeristy, Shahrekord P.O. Box 115, Iran)

Abstract

An analysis is performed in this research to obtain the natural frequencies of a graphene-platelet-reinforced composite plate at nanoscale. To this end, the nonlocal elasticity theory is applied. A composite laminated plate is considered where each layer is reinforced with GPLs. The amount of GPLs may be different between the layers, which results in functionally graded media. To establish the governing equations of the plate, a quasi-3D plate model is used, which takes the non-uniform shear strains as well as normal strain through the thickness into account. With the aid of the Hamilton principle, the governing equations of the plate are established. For the case of a plate that is simply supported all around, natural frequencies are obtained using the well-known Navier solution method. The results of this study are compared with the available data in the open literature, and, after that, novel numerical results are provided to explore the effects of different parameters. It is depicted that, with the introduction of GPLs in the matrix of the composite media, the natural frequencies of the plate enhance. Also, a proper graded pattern in GPL-reinforced composite plates, i.e., an FG-X pattern, results in the maximum frequencies of the plate. In addition, the introduced quasi-3D plate theory is accurate in the estimation of the natural frequencies of thick nanocomposite plates at nanoscale.

Suggested Citation

  • Yunhe Zou & Yaser Kiani, 2023. "Vibrations of Nonlocal Polymer-GPL Plates at Nanoscale: Application of a Quasi-3D Plate Model," Mathematics, MDPI, vol. 11(19), pages 1-18, September.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:19:p:4109-:d:1250172
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/19/4109/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/11/19/4109/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ammar Melaibari & Ahmed Amine Daikh & Muhammad Basha & Ahmed Wagih & Ramzi Othman & Khalid H. Almitani & Mostafa A. Hamed & Alaa Abdelrahman & Mohamed A. Eltaher, 2022. "A Dynamic Analysis of Randomly Oriented Functionally Graded Carbon Nanotubes/Fiber-Reinforced Composite Laminated Shells with Different Geometries," Mathematics, MDPI, vol. 10(3), pages 1-24, January.
    2. Farzad Ebrahimi & Hosein Ezzati, 2023. "A Machine-Learning-Based Model for Buckling Analysis of Thermally Affected Covalently Functionalized Graphene/Epoxy Nanocomposite Beams," Mathematics, MDPI, vol. 11(6), pages 1-13, March.
    3. Mahmure Avey & Nicholas Fantuzzi & Abdullah Sofiyev, 2022. "Mathematical Modeling and Analytical Solution of Thermoelastic Stability Problem of Functionally Graded Nanocomposite Cylinders within Different Theories," Mathematics, MDPI, vol. 10(7), pages 1-11, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mahmure Avey & Nicholas Fantuzzi & Abdullah H. Sofiyev, 2023. "Analytical Solution of Stability Problem of Nanocomposite Cylindrical Shells under Combined Loadings in Thermal Environments," Mathematics, MDPI, vol. 11(17), pages 1-21, September.
    2. Gamal S. Abdelhaffez & Ahmed Amine Daikh & Hussein A. Saleem & Mohamed A. Eltaher, 2023. "Buckling of Coated Functionally Graded Spherical Nanoshells Rested on Orthotropic Elastic Medium," Mathematics, MDPI, vol. 11(2), pages 1-25, January.
    3. Shaoping Bi & Enming Zhang & Masoud Babaei & Francesco Tornabene & Rossana Dimitri, 2023. "The Influence of GPL Reinforcements on the Post-Buckling Behavior of FG Porous Rings Subjected to an External Pressure," Mathematics, MDPI, vol. 11(11), pages 1-21, May.
    4. Emad E. Ghandourah & Ahmed A. Daikh & Abdulsalam M. Alhawsawi & Othman A. Fallatah & Mohamed A. Eltaher, 2022. "Bending and Buckling of FG-GRNC Laminated Plates via Quasi-3D Nonlocal Strain Gradient Theory," Mathematics, MDPI, vol. 10(8), pages 1-37, April.
    5. Krzysztof Kamil Żur & Jinseok Kim & Junuthula N. Reddy, 2022. "Special Issue of Mathematics : Analytical and Numerical Methods for Linear and Nonlinear Analysis of Structures at Macro, Micro and Nano Scale," Mathematics, MDPI, vol. 10(13), pages 1-2, June.
    6. Ammar Melaibari & Salwa A. Mohamed & Amr E. Assie & Rabab A. Shanab & Mohamed A. Eltaher, 2022. "Free Vibration Characteristics of Bidirectional Graded Porous Plates with Elastic Foundations Using 2D-DQM," Mathematics, MDPI, vol. 11(1), pages 1-26, December.
    7. Doaa Atta & Ahmed E. Abouelregal & Fahad Alsharari, 2022. "Thermoelastic Analysis of Functionally Graded Nanobeams via Fractional Heat Transfer Model with Nonlocal Kernels," Mathematics, MDPI, vol. 10(24), pages 1-24, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:19:p:4109-:d:1250172. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.